# day/dydd 224 at 7puzzleblog.com T he Main Challenge

Today’s task is to multiply two numbers together, then either add or subtract the third number to achieve the target answer of 37.

Using the formula (a×b)±c, where a, b and c are three unique digits from 1-9, one way of achieving 37 is (7×5)+2; can you find the other SEVEN ways?

[Note: (7×5)+2 = 37 and  (5×7)+2 = 37 counts as just ONE way.] The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from up to 84.

The 5th & 6th rows of the playing board contain the following fourteen numbers:

5   6   7   12   16   18   20   21   33   49   50   56   81   84

From the list, which three different numbers have a sum of 100? The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive integer can be made by adding up to four square numbers.

For example, 7 can be made by 2²+1²+1²+1² (or 4+1+1+1).

There is only ONE way to make 224 when using Lagrange’s Theorem. Can you find it? The Mathematically Possible Challenge

Using 46 and once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

13    26    39    52    65    78    91    104    117    130

#13TimesTable The Target Challenge

Can you arrive at 224 by inserting 127 and 7 into the gaps on each line?

•  ◯×◯²×(◯+◯) = 224
•  ◯⁵×◯³×◯²÷◯ = 224   